Analytic Foliations and the Theory of Levels.
Growth of leaves.
Leafwise hyperbolicity; a correction.
Leafwise hyperbolicity of proper foliations.
Smoothability of proper foliations
Compact, -foliated manifolds of codimension one, having all leaves proper, are shown to be -smoothable. More precisely, such a foliated manifold is homeomorphic to one of class . The corresponding statement is false for foliations with nonproper leaves. In that case, there are topological distinctions between smoothness of class and of class for every nonnegative integer .
Leaves of Markov local minimal sets in foliations of codimension one.
The authors continue their study of exceptional local minimal sets with holonomy modeled on symbolic dynamics (called Markov LMS [C-C 1]). Here, an unpublished theorem of G. Duminy, on the topology of semiproper exceptional leaves, is extended to every leaf, semiproper or not, of a Markov LMS. Other topological results on these leaves are also obtained.
Tischler fibrations of open foliated sets
Let be a closed, foliated manifold, and let be an open, connected, saturated subset that is a union of locally dense leaves without holonomy. Supplementary conditions are given under which admits an approximating (Tischler) fibration over . If the fibration exists, conditions under which the original leaves are regular coverings of the fibers are studied also. Examples are given to show that our supplementary conditions are generally required.
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